**Abstract:** Perturbed Kepler problem is formulated in terms of quaternions, resulting in Kustaanheimo-Stiefel equation. Assuming the perturbation to be proportionalto epsilon (a small parameter), the equation is then solved, iteratively, by expanding the solution in powers of epsilon. We first deal with the autonomous case, and then proceed to the case of explicitly time-dependent perturbations, including those in resonance with the satellite's motion.